Abstract

Dipolar Bose and Fermi gases, which are currently being studied extensively experimentally and theoretically, interact through anisotropic, long-range potentials. Here, we replace the long-range potential by a zero-range pseudopotential that simplifies the theoretical treatment of two dipolar particles in a harmonic trap. Our zero-range pseudopotential description reproduces the energy spectrum of two dipoles interacting through a shape-dependent potential under external confinement very well, provided that sufficiently many partial waves are included, and readily leads to a classification scheme of the energy spectrum in terms of approximate angular momentum quantum numbers. The results may be directly relevant to the physics of dipolar gases loaded into optical lattices.

Atom-atom scattering of bosonic one-dimensional (1D) atoms has been modeled successfully using a zero-range {delta}-function potential, while that of bosonic 3D atoms has been modeled successfully using Fermi-Huang's regularized s-wave pseudopotential. Here, we derive the eigenenergies of two spin-polarized 1D fermions under external harmonic confinement interacting through a zero-range potential, which only acts on odd-parity wave functions, analytically. We also present a divergent-free zero-range potential treatment of two spin-polarized 3D fermions under harmonic confinement. Our pseudopotential treatments are verified through numerical calculations for short-range model potentials.

The effect of strongly repulsive interactions on the tunneling amplitude of hard-sphere (HS) bosons confined in a simple cubic optical lattice plus tight external harmonic confinement in continuous space is investigated. The quantum variational Monte Carlo (VMC) and the variational path integral (VPI) Monte Carlo techniques are used at zero temperature. The effects of the lattice spacing on the tunneling amplitude are also considered. The occupancies of the lattice sites as a function of the repulsion between the bosons are further revealed. Our chief result is that for a small number of bosons (N=8) the overlap of the wave functionsmore » in neighboring wells practically does not change with an increase of the repulsive interactions and changes only minimally for a larger number of particles (N=40). The tunneling amplitude rises with a reduction in the lattice spacing. In addition, the occupancy of the center of the trap decreases in favor of a rise in the occupancy of the lattice sites at the edges of the trap with increasing HS repulsion. Further, it was found that the energy per particle at certain optical-lattice barrier heights is insensitive to the number of particles and variations in the HS diameter of the bosons. In order to support our results, we compare the VMC results with corresponding VPI results.« less

We extend a model of two-center interference to include the superposition of opposite orientations in aligned polar molecules. We show that the position of the minimum in the harmonic spectrum from both aligned and oriented CO depends strongly on the relative recombination strength at different atoms, not just the relative phase. We reinterpret the minimum in aligned CO as an interference between opposite orientations, and obtain good agreement with numerical calculations. Inclusion of the first-order Stark effect shifts the position of the interference minimum in aligned CO even though aligned molecules do not posses total permanent dipoles. We explain themore » shift in terms of the phase that the electron of oriented CO accumulates due to the Stark effect.« less

The unequal-quark-mass problem of excited ..lambda.. and ..sigma.. states is treated through a multichannel generalization of a relativistic Bethe-Salpeter treatment of the simpler (equal-mass) problem of N and ..delta.. as well as meson states recently found to give excellent fits to the corresponding spectra. The present fits to the ..lambda.. and ..sigma.. masses are fully in tune with the quality of the N/sub L/, and ..delta../sub L/ results, as evidenced by the highly consistent values of the appropriate universal function F(M) representing the central (mass)/sup 2/ for each N supermultiplet, calculated with the same reduced spring constant and quark massesmore » as employed earlier for N/sub L/, ..delta../sub L/, and meson states. These F(M) values now include the one-gluon-exchange corrections which help in improving the F(M) regularities over the pure harmonic-oscillator prediction. The F(M) representation also brings out rather succintly a modest symmetry-breaking trend (approx.5--10 %) at the collective supermultiplet level with little scatter among individual members.« less